What Is Compound Interest?
Compound interest is the interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which only earns on the original amount, compound interest lets your money grow exponentially over time. Albert Einstein reportedly called compound interest "the eighth wonder of the world," and for good reason: it is the single most powerful force behind long-term wealth building.
The Compound Interest Formula
Where:
A = Final amount
P = Principal (initial investment)
r = Annual interest rate (decimal)
n = Number of times interest is compounded per year
t = Number of years
Step-by-Step Example
You invest $5,000 at 6% annual interest, compounded monthly, for 10 years:
- Identify values: P = $5,000, r = 0.06, n = 12, t = 10
- Plug into formula: A = 5000 × (1 + 0.06/12)12×10
- Simplify inside parentheses: A = 5000 × (1.005)120
- Calculate the exponent: (1.005)120 ≈ 1.8194
- Multiply: A = 5000 × 1.8194 = $9,097.01
Your $5,000 grew to over $9,097 — that is $4,097 in interest earned without any additional deposits.
How Compounding Frequency Affects Growth
The more frequently interest compounds, the more you earn. Here is a comparison of $10,000 invested at 5% for 10 years under different compounding frequencies:
| Compounding Frequency | n (per year) | Final Amount | Interest Earned |
|---|---|---|---|
| Annually | 1 | $16,288.95 | $6,288.95 |
| Semi-annually | 2 | $16,386.16 | $6,386.16 |
| Quarterly | 4 | $16,436.19 | $6,436.19 |
| Monthly | 12 | $16,470.09 | $6,470.09 |
| Daily | 365 | $16,486.65 | $6,486.65 |
Compound Interest vs Simple Interest
Simple interest is calculated only on the principal, while compound interest is calculated on the principal plus all previously earned interest. Over short periods the difference is small, but over decades it becomes enormous.
| Year | Simple Interest (5%) | Compound Interest (5%) | Difference |
|---|---|---|---|
| 1 | $10,500 | $10,500 | $0 |
| 5 | $12,500 | $12,763 | $263 |
| 10 | $15,000 | $16,289 | $1,289 |
| 20 | $20,000 | $26,533 | $6,533 |
| 30 | $25,000 | $43,219 | $18,219 |
After 30 years, compound interest produces 73% more than simple interest on the same $10,000 investment at 5%.
The Rule of 72
The Rule of 72 is a quick mental shortcut to estimate how long it takes for an investment to double:
| Interest Rate | Rule of 72 Estimate | Actual Years |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
Practical Tips for Maximizing Compound Interest
- Start early: Time is the most important variable — even small amounts invested early outperform larger amounts invested later.
- Reinvest dividends: Always reinvest earnings so they compound along with your principal.
- Choose higher compounding frequency: Monthly or daily compounding earns more than annual compounding.
- Be consistent: Regular contributions amplify the compounding effect dramatically.
- Minimize fees: High fees reduce the effective rate and erode compounding gains over time.
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